Existence and properties of quadratic solitons in anisotropic media: Variational approach

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Abstract
Stationary quadratic solitons associated with second harmonic generation in optically anisotropic media have been investigated both numerically and analytically using the variational approach. The solitons were found to have elliptical shapes, both for the fundamental and second harmonic, and their approximate beam waists and amplitudes as a function of the anisotropy and the soliton parameter were found. The important limits of anisotropic diffraction were compared to the well-known model of isotropic diffraction. The stability of anisotropic solitons was addressed via the Vakhitov-Kolokolov criterion and the regions of parameter space for which the solitons are stable were identified. Direct numerical simulations of the coupled field equations were performed to illustrate the existence, stability, and ellipticity of anisotropic quadratic solitons. In general, good agreement was found between approximate analytical approaches and numerical experiments.